Prove that there exists a positive integer N such that for all n ≥ N , we have2023n ≤ n!. You may use, without proof, the fact that 20236000 ≤ 6000!
Question
Solution 1
To prove this, we will use the concept of mathematical induction.
Step 1: Base Case We are given that 20236000 ≤ 6000!. Since 2023 < 20236000, we can say that 2023*6000 ≤ 6000!. So, we can take our base case as N = 6000.
Step 2: Inductive Step Assume that the statement is true for some k ≥ N, i.e. Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
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